Modern Theory, Part Two

Diversification and the Market Portfolio This is the second in a ten-part series exploring the implications of (MPT) for common investment decisions faced by individuals. This part focuses on two ma- jor concepts: diversification and the market portfolio. by Donald R. Chambers

odern Portfolio Theory pro- as diversifiable, non-systematic, Diversification Defined. Most Mvides a rigorous understand- non-market or unique . Idiosyn- investment professionals use the ing of what diversification is and cratic risk is any fluctuation in an as- term “diversification” to represent how it works to improve investment set’s return that is not caused by (or the spreading of one’s wealth into a opportunities. MPT also shows how at least correlated with) the move- variety of investments. For example, to create the portfolio that contains ments in the overall market. An ex- a broker might say “I think stocks as much diversification as possible: ample of idiosyncratic risk is when are getting a little overvalued now the market portfolio. In and it is time to diversify doing so, MPT provides a The enormous breakthrough in MPT: Inves- a little by placing some powerful prescription that money in Treasury bills.” is applicable to virtually tors can optimize their portfolios by select- MPT uses a more every investor. MPT tells ing from only two investment alternatives precise definition of us exactly which risky diversification that is assets we should hold and (the market portfolio and riskless assets). more useful for this in which proportions we analysis. Diversification should hold them! a firm drops 10 percent because it is the spreading of one’s wealth into Briefly, the market portfolio announces bad earnings. When a risky assets that have some level of is that portfolio that contains all firm drops 10 percent because the imperfect correlation. Imperfect cor- investable assets that contain risk— overall stock market plunged, it is relation is when two variables have and holds them in proportion to market or . at least some chance of not always their size. is also known as moving in the same direction and in An investor who implements this non-diversifiable, systematic or the same proportion to each other. prescription from MPT for her in- beta risk. The market risk of an Virtually all stocks are imper- vestment decisions can ignore over investment is all fluctuations in the fectly correlated with each other and 90 percent of the complexities, deci- investment’s value that are caused therefore provide at least some level sions, and wasted time of traditional by or correlated with movements in of diversification when combined investment analysis and can focus the overall market. into a portfolio. The imperfect cor- on the one unambiguously beneficial Virtually all stocks of individual relations mean that their differences objective: diversification. firms have both market risk and in returns may at least occasionally idiosyncratic risk—which combine offset each other to some degree Market and Idiosyncratic . to form their total risk. For most if the assets are combined into a Part 1 of this series introduced stocks, the idiosyncratic risk is portfolio. That is the essence of MPT’s distinction of two types of substantially larger than the market diversification. risk: idiosyncratic risk and market risk. The market portfolio contains Putting it another way, diver- (systematic) risk. market risk—but by definition con- sification is unambiguously good. Idiosyncratic risk is also known tains no idiosyncratic risk. The idea is that the idiosyncratic risk (i.e., the diversifiable risk as Author Donald R. Chambers is the Walter E. Hanson/KPMG Professor of introduced in Part 1) of one asset Finance at Lafayette College in Easton, Pennsylvania. offsets at least some of the idiosyn- Research Reports, October 18, 2010

cratic risk of another asset—causing Perfectly Positively Correlated The idea that perfectly positively idiosyncratic risk to disappear from Assets Do Not Diversify. Usually, correlated assets do not provide the portfolio. combining risky assets into a portfo- diversification is illustrated with a MPT predicts that investors can lio provides diversification. But to il- solid line in Figure 1. Asset A has lower their risk without lowering their lustrate the principles involved, let’s relatively low risk and low expected expected returns through diversifica- first look at the extreme case where return. Asset B has higher risk and tion. It is the closest thing to the pro- returns are perfectly correlated and higher . Perhaps as- verbial “free lunch” that a financial there is no diversification. set A is an unleveraged investment economist can find. The returns of one share of IBM in an S&P 500 fund and Asset B is That is why diversification are perfectly correlated with the re- an investment that uses leverage and should be the primary goal of the turns of another share of IBM since also tracks the S&P 500 closely. investor. they are identical. Any unexpectedly Notice that moving money high or unexpectedly low outcomes from asset B to asset A lowers risk. The Riskless Asset Reduces in the one share are identical to the But this risk reduction is not due Risk but Does Not Diversify. As unexpected outcomes in the other to diversification. There are no explained in the first part of this share. Thus, holding a portfolio idiosyncratic risks offsetting each series, MPT prescribes that investors consisting only of many shares of other and disappearing. And MPT should hold only two assets: the the same stock does not provide predicts that, unlike the risk reduc- market portfolio and the riskless diversification. tion gained through diversification, asset. (Formally, this idea is often A less trivial example would be this risk reduction will come at the referred to as the “two fund separa- the combination of mutual funds expense of lower expected return. tion theorem.”) or other products that closely track Investing in T-bills (U.S. Trea- the same index such as an index of Imperfectly Correlated Assets Do sury bills), money market funds, or pharmaceutical stocks. Since those Diversify Risk. The diversification money market accounts (i.e., riskless assets are nearly perfectly positively obtained by combining risky assets assets) reduces risk. But the returns correlated, there would be virtually depends on the correlation of those of riskless assets are fixed (in the no diversification from combining assets. Generally, when the correla- short run) and therefore they do not them into a portfolio. tion is lower the diversification is ever have unexpectedly high returns and—in the pure sense of the word—cannot provide diversifica- Figure 1. Perfectly Correlated Assets tion. A T-bill might offer a posi- tive return when all other risky assets decline, but it can not offer an unexpectedly high return. This seemingly minor point is actually an essential observation in estab- Expected Return lishing the enormous breakthrough B in MPT that investors can optimize their portfolios by selecting from A portfolio consisting only two investment alternatives mostly of asset B (the market portfolio and riskless assets). Riskless assets such as T-bills do not have idiosyncratic risk. There- A portfolio with 50% fore, riskless assets cannot offset the A and 50% B idiosyncratic risks of risky assets and make the risk “disappear” in a port- folio. Simply put, riskless assets do not A portfolio consisting provide diversification. Diversifica- mostly of asset A tion can lower risk without lower- A ing expected returns. MPT predicts that investing a riskless asset will lower risk, but only at the expense of lowered expected returns. Total Risk

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greater. If an investor puts half his that risk is being reduced without earn high returns without a “valid” or her money in one risky asset with lowering the expected return! MPT economic purpose or without rea- typical annual return fluctuations views the process of diversified in- sonable financial expectations. of 40 percent and the other half in vesting as a battle for simultaneously Consider Mr. Smart, who places another asset with the same general reducing risk without reducing most of his wealth in a diversified magnitude of fluctuations (i.e., 40 expected return. stock portfolio. Mr. Smart does percent), the fluctuations of the not view the stock market as being resulting portfolio can be 0 percent, Market Risk Is Rewarded, Idiosyn- wildly undervalued or overvalued. 40 percent or anywhere in between cratic Risk Is Not! Here is the most He views the stock market as being depending on how the assets cor- single important prediction of MPT. risky but on average expects that the relate to each other. Investors who bear systematic risk stock market will outperform risk- The interrelationship of cor- will earn higher expected returns. less investment opportunities. relations and diversification can be But investors who bear additional Mr. Smart is performing a valid demonstrated with the mathematics idiosyncratic risk will not earn economic function (bearing the of risk and illustrated with charts. higher expected returns. Bearing systematic risk of an economy) and Figure 2 illustrates this concept with idiosyncratic risks will sometimes anticipates an appropriate potential low correlation as illustrated by the generate high returns, sometime reward. He has selected a level of dotted and curved line connecting generate low returns, but on average risk based on his reasonable antici- assets C and D. will not increase expected return. pation of higher expected return. The curve labeled “low correla- The major prescription of MPT Mr. Smart is bearing risk, and even tion” in Figure 2 illustrates the key becomes clear. Avoid idiosyncratic if he is bearing a large amount of concept of combining imperfectly risk by diversifying as much as pos- risk he is not speculating. correlated assets such as two typical sible. What is speculation? There are stocks. Diversification is illustrated two major types. One is bearing as the “bending” of the portfolio in Speculation. Many practitioners idiosyncratic risks. The other is the direction of less risk (left). equate speculation with exces- bearing the wrong levels of risk, The key point being illustrated sive risk. But a more meaningful whether too high or too low. with the dotted curve in Figure 2 is definition is that it is an attempt to As an example of the first type, consider Mr. Stock-Picker. He de- cides not to diversify and therefore Figure 2. Diversification bears idiosyncratic risk. He puts a lot of his money in a handful of stocks that he thinks will outper- form the market. Mr. Stock-Picker is hoping that he will be rewarded with high returns. But according to MPT he is speculating based on Expected hope. He is like a casino gambler Return D who places money on a roulette table but who has no rational reason Low to believe that the expected returns correlation will be exceptional. As to the second type, consider Reduced risk Mr. Market-Timer. Sometimes he bears great systematic risk through Perfect positive leverage (when he thinks the correlation market is undervalued). Sometimes he places his money in cash (when he thinks the market is overval- ued). Mr. Market-Timer should be viewed as speculating both when C he is over-exposed to risk and even when all of his money is in cash! The reason is that his risk taking is based on unrealistic or unfounded Total Risk return expectations.

EX—3 Research Reports, October 18, 2010

What Does the Market Portfolio located in their own nation and over regarding diversification is that a Look Like? MPT establishes that 99 percent in assets located outside diversified portfolio can be obtained the perfectly diversified portfolio— their home country. with perhaps 20 or 30 stocks. That is the market portfolio—holds every Another potential problem is not quite the case. possible risky asset or security and that in practice including all assets A portfolio of 100 securities will holds each in direct proportion to is not always feasible since not all eliminate about 90 percent of the id- its size. In theory this requires hold- assets are investable. Queasy Bakery iosyncratic risks of the securities in ing, literally, all risky assets: stocks, Corp. might be a family held busi- the portfolio. But even a portfolio of long term bonds, defaultable bonds, ness. Maybe Queasy Bakery Corp. 400 securities will still retain about 5 real estate, funds, commodi- is located in a country that does not percent of its idiosyncratic risks. ties, private equity, collectibles and allow foreign investment. Thus, excellent diversifica- so forth. In theory this also means And holding a little of every asset tion should involve thousands of holding every risky asset in propor- that can be purchased is not practi- underlying positions. For all but the tion to its total size. cally feasible due to the transactions super-rich, a high level of diversifi- If Goliath Bank Corp. is one costs of assembling and managing cation requires the use of diversi- thousand times the size of Queasy such a massive number of positions. fied mutual funds, exchange traded Bakery Corp. then a perfectly diver- But increasingly there are some funds, or derivative products that sified portfolio must have a position well-diversified and cost-effective contain over a thousand underlying in Goliath Bank that is one thou- investment funds that are providing positions. sand times the size of the position in impressive diversification. High lev- Queasy Bakery Corp. els of diversification are increasingly Conclusions. Diversification is The idea of holding each secu- possible and cost effective. the reduction of idiosyncratic risk rity in proportion to its size also But perfect diversification is not through combining imperfectly applies to types of assets and groups literally possible. correlated assets into a portfolio. of assets. Thus, industry Perfect diversification and sectors should be For all but the super-rich, a high level of is the elimination of all held in proportion to idiosyncratic risks. It is their sizes. Real estate, diversification requires the use of diversi- accomplished by holding private equity, commodi- fied mutual funds, exchange traded funds, the market portfolio. The ties and hedge funds market portfolio contains should be held in propor- or derivative products. all investable assets and tion to their sizes. And holds those assets in pro- assets grouped by country should So, the market portfolio de- portion to their available size. also be held in proportion to their scribed above is really just an ideal MPT predicts that bearing sizes. Note that the combination of towards which each investor should systematic risks is the only way to all the portfolios of all investors in aspire in the absence of rational increase expected returns. MPT im- the world is the market portfolio. reasons to do otherwise. In practice plies that investors should focus on And all investors should hold the it means avoiding the temptation diversification and should eschew same portfolio. to intentionally take idiosyncratic efforts to speculate on idiosyncratic One of the most controver- risks, and it means investing in risks. sial prescriptions of MPT is that very large collections of assets (with The remaining parts of this series every investor’s portfolio should be individual asset weightings that are build on the concepts included in invested in the securities of each in proportion to size). this discussion of diversification country according to that country’s and the market portfolio. Risk is a relative economic size. Thus every How Many Securities Does It Take key element of virtually all parts of portfolio should be the same as to Be Well Diversified? For many MPT. And risk is best understood the market portfolio and should investors, their risky portfolio is through the statistical measure be 30 percent-40 percent invested primarily comprised of securities known as standard deviation. in US based assets and only a few such as stocks (for example, as held The purpose of the next (i.e., percentage points of assets should inside of mutual funds). While in third) part of this series is to be invested in all of the countries theory, the portfolio should contain introduce and clarify the concept of Africa and South America com- every stock and other security in the of standard deviation, and then bined. MPT, in its simplest form, world, in practice this is too costly build a solid, structured and precise prescribes that a citizen of a small and the investor will hold a some- understanding of risk and of the nation should invest less than 1 what small sampling of those stocks. tradeoff between risk and expected percent of their portfolio in assets One of the most common errors return.

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